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学者姓名：王伟伟
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Abstract ：
This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. Suppose that the initial data is a small perturbation near the equilibrium state (rho(infinity),0,theta(infinity),zeta), where rho(infinity)>0, theta(infinity)theta I discussed in Wang and Wen (Sci China Math 65:1199-1228 (2022).
Keyword ：
Compressible combustion fluids Compressible combustion fluids Energy estimates Energy estimates Global strong solutions Global strong solutions Optimal temporal decay rates Optimal temporal decay rates
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| GB/T 7714 | Fu, Shengbin , Huang, Wenting , Wang, Weiwei . Optimal temporal decay rates of solutions for combustion of compressible fluids [J]. | ANALYSIS AND MATHEMATICAL PHYSICS , 2024 , 14 (6) . |
| MLA | Fu, Shengbin 等. "Optimal temporal decay rates of solutions for combustion of compressible fluids" . | ANALYSIS AND MATHEMATICAL PHYSICS 14 . 6 (2024) . |
| APA | Fu, Shengbin , Huang, Wenting , Wang, Weiwei . Optimal temporal decay rates of solutions for combustion of compressible fluids . | ANALYSIS AND MATHEMATICAL PHYSICS , 2024 , 14 (6) . |
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Recently, Li-Fu-Wang (Li et al., 2022) established the optimal temporal decay rates of solutions near the equilibrium state to the 3D compressible magnetohydrodynamic system with nonlinear damping alpha|u|(beta-1)u for beta >= 3. In this paper, we further extend Li-Fu-Wang's result to the case beta > 1 by finer energy estimates.
Keyword ：
Compressible magnetohydrodynamic fluids Compressible magnetohydrodynamic fluids Global-in-time existence Global-in-time existence Nonlinear damping Nonlinear damping Optimal time-decay rates Optimal time-decay rates Uniqueness Uniqueness
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| GB/T 7714 | Zeng, Ruixin , Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping [J]. | APPLIED MATHEMATICS LETTERS , 2024 , 156 . |
| MLA | Zeng, Ruixin 等. "Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping" . | APPLIED MATHEMATICS LETTERS 156 (2024) . |
| APA | Zeng, Ruixin , Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping . | APPLIED MATHEMATICS LETTERS , 2024 , 156 . |
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The stability and large-time behavior problem on the magneto-micropolar equations has evoked a considerable interest in recent years. In this paper, we study the stability and exponential decay near magnetic hydrostatic equilibrium to the two-dimensional magneto-micropolar equations with partial dissipation in the domain O= T x R. In particular, we takes advantage of the geometry of the domain T x R to divide u into zeroth mode and the nonzero modes, and obey a strong version of the Poincare's inequality, which plays a crucial role in controlling the nonlinearity. Moreover, we find that the oscillation part of the solution decays exponentially to zero. Finally, our result mathematically verifies that the stabilization effect of a background magnetic field on magneto-micropolar fluids.
Keyword ：
large-time behavior large-time behavior Magneto-micropolar fluids Magneto-micropolar fluids partial dissipation partial dissipation stability stability
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| GB/T 7714 | Zhang, Yajie , Wang, Weiwei . Stability and exponential decay for the 2D magneto-micropolar equations with partial dissipation [J]. | APPLICABLE ANALYSIS , 2023 , 103 (2) : 432-444 . |
| MLA | Zhang, Yajie 等. "Stability and exponential decay for the 2D magneto-micropolar equations with partial dissipation" . | APPLICABLE ANALYSIS 103 . 2 (2023) : 432-444 . |
| APA | Zhang, Yajie , Wang, Weiwei . Stability and exponential decay for the 2D magneto-micropolar equations with partial dissipation . | APPLICABLE ANALYSIS , 2023 , 103 (2) , 432-444 . |
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Recently, Hattori-Lagha established the global existence and asymptotic behavior of the solutions for a three-dimensional compressible chemotaxis system with chemoattractant and repellent (Hattori and Lagha in Discrete Contin. Dyn. Syst. 41(11):5141-5164, 2021). Motivated by Hattori-Lagha's work, we further investigated the optimal time-decay rates of strong solutions with small perturbation to the three-dimensional Keller-Segel system coupled to the compressible Navier-Stokes equations, which models for the motion of swimming bacteria in a compressible viscous fluid. First, we reformulate the system into a perturbation form. Then we establish a prior estimates of solutions and prove the existence of the global-in-time solutions based on the local existence of unique solutions. Finally, we will establish the optimal time-decay rates of the nonhomogeneous system by the decomposition technique of both low and high frequencies of solutions as in (Wang and Wen in Sci. China Math., 2020, https://doi.org/10.1007/s11425-020-1779-7). Moreover, the decay rate is optimal since it agrees with the solutions of the linearized system.
Keyword ：
Compressible chemotactic fluids Compressible chemotactic fluids Fourier theory Fourier theory Global existence Global existence Optimal time-decay rates Optimal time-decay rates Uniqueness Uniqueness
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| GB/T 7714 | Guo, Yuting , Sun, Rui , Wang, Weiwei . Optimal time-decay rates of the Keller-Segel system coupled to compressible Navier-Stokes equation in three dimensions [J]. | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
| MLA | Guo, Yuting 等. "Optimal time-decay rates of the Keller-Segel system coupled to compressible Navier-Stokes equation in three dimensions" . | BOUNDARY VALUE PROBLEMS 2022 . 1 (2022) . |
| APA | Guo, Yuting , Sun, Rui , Wang, Weiwei . Optimal time-decay rates of the Keller-Segel system coupled to compressible Navier-Stokes equation in three dimensions . | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
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This paper focuses on the Rayleigh-Taylor instability in the system of equations of the two-dimensional nonhomogeneous incompressible elasticity fluid in a horizontal periodic domain with infinite height. First, we use variational method to construct (linear) unstable solutions for the linearized elastic Rayleigh-Taylor problem. Then, motivated by the Grenier's idea in [1.0], we further construct approximate solutions with higher-order growing modes to the elastic Rayleigh-Taylor problem due to the absence of viscosity in the system, and derive the error estimates between both the approximate solutions and nonlinear solutions of the elastic Rayleigh-Taylor problem. Finally, we prove the existence of escape points based on the bootstrap instability method of Hwang-Guo in [25], and thus obtain the nonlinear Rayleigh- Taylor instability result, which presents that the Rayleigh-Taylor instability can occur in elasticity fluids with small elasticity coefficient. (C) 2022 Elsevier Inc. All rights reserved.
Keyword ：
Approximate solutions Approximate solutions Bootstrap instability method Bootstrap instability method Incompressible elasticity fluids Incompressible elasticity fluids Rayleigh-Taylor instability Rayleigh-Taylor instability
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| GB/T 7714 | Hua, Zhiwei , Jiang, Han , Zhang, Xuyan et al. On Rayleigh-Taylor instability in nonhomogeneous incompressible elasticity fluids [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2022 , 515 (2) . |
| MLA | Hua, Zhiwei et al. "On Rayleigh-Taylor instability in nonhomogeneous incompressible elasticity fluids" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 515 . 2 (2022) . |
| APA | Hua, Zhiwei , Jiang, Han , Zhang, Xuyan , Wang, Weiwei . On Rayleigh-Taylor instability in nonhomogeneous incompressible elasticity fluids . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2022 , 515 (2) . |
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In this paper we investigate the existence and time-decay rates of strong solutions with small perturbation to the systems of equations of a compressible magneto-hydrodynamic fluid with nonlinear damping. First we reformulate the system into a perturbation form. Then we establish a priori estimates of solutions, and prove the existence of the global-in-time based on the local existence of unique solutions. Finally we will establish the optimal time-decay rates of the non-homogeneous system by constructing some decay estimates of the linearized system based on the decomposition technique of both the low and high frequencies of solutions as in [40]. (C) 2022 Elsevier Inc. All rights reserved.
Keyword ：
Fourier theory Fourier theory Global existence and uniqueness Global existence and uniqueness magnetohydrodynamic fluids magnetohydrodynamic fluids Optimal time-decay rates Optimal time-decay rates Three-dimensional compressible Three-dimensional compressible
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| GB/T 7714 | Li, Jiedi , Fu, Shengbin , Wang, Weiwei . On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2022 , 515 (2) . |
| MLA | Li, Jiedi et al. "On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 515 . 2 (2022) . |
| APA | Li, Jiedi , Fu, Shengbin , Wang, Weiwei . On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2022 , 515 (2) . |
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Recently, Gao and Yao established the global existence and temporal decay rates of solutions for a system of compressible Hall-magnetohydrodynamic fluids (Gao and Yao in Discrete Contin. Dyn. Syst. 36: 3077-3106, 2016). However, because of the difficulty of derivative loss in the nonlinear terms, Gao and Yao could not provide the temporal decay for the highest-order derivatives of classical solutions. In this paper, motivated by the decomposition technique of both low and high frequencies of solutions in (Wang and Wen in Sci. China Math. 65: 1199-1228 2022), we further derive the temporal decay for the highest-order derivatives of the strong solutions. Moreover, the decay rate is optimal, since it agrees with the solutions of the linearized system.
Keyword ：
Compressible Hall-magnetohydrodynamic fluids Compressible Hall-magnetohydrodynamic fluids Fourier theory Fourier theory Highest-order derivatives Highest-order derivatives Optimal time-decay rates Optimal time-decay rates
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| GB/T 7714 | Sun, Rui , Guo, Yuting , Wang, Weiwei . Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations [J]. | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
| MLA | Sun, Rui et al. "Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations" . | BOUNDARY VALUE PROBLEMS 2022 . 1 (2022) . |
| APA | Sun, Rui , Guo, Yuting , Wang, Weiwei . Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations . | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
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It is well-known that the Cauchy problem of the compressible liquid crystals flow admits a unique global-in-time solution, belonging to C-0(R-0(+) , H-l(R-3)) with l >= 3; moreover the lower-order or higher-order derivative of solution enjoys the same decay-in-time rate as well as the linear solution (i.e., the solution of the corresponding linear problem). In this paper we further prove that highest-order derivative of the unique solution also enjoys the same decay-in-time rate as well as the linear solution by developing new analytical skills. In other words, the optimal decay rate for the highest-order derivative of solution can be also obtained. (C) 2021 Elsevier Ltd. All rights reserved.
Keyword ：
Cauchy problem Cauchy problem Large-time behavior Large-time behavior Liquid crystals Liquid crystals Optimal decay rate Optimal decay rate
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| GB/T 7714 | Xiong, Jing , Wang, Jialiang , Wang, Weiwei . Decay for the equations of compressible flow of nematic liquid crystals [J]. | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2021 , 210 . |
| MLA | Xiong, Jing et al. "Decay for the equations of compressible flow of nematic liquid crystals" . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 210 (2021) . |
| APA | Xiong, Jing , Wang, Jialiang , Wang, Weiwei . Decay for the equations of compressible flow of nematic liquid crystals . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2021 , 210 . |
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In this paper, we consider the large time behavior of the Cauchy problem for the three-dimensional isentropic compressible magnetohydrodynamic (MHD) equations. The global existence of smooth solutions for the 3D compressible MHD equations has been proved by Chen-Tan [6], under the condition that the initial data are close to the constant equilibrium state in the Sobolev space H-3. However, to our best knowledge, the decay estimate of the highest-order spatial derivatives of the solution to the compressible MHD equations has not been solved. The main goal in this paper is to give a positive answer to this problem. Exactly, under the assumption that the initial perturbation is small in H-l(R-3) boolean AND (B) over dot(2,infinity)(-s)(R-3) with l >= 3, s is an element of inverted right perpendicular0,5/2inverted left perpendicular, combining the spectral analysis on the semigroup generated by the linear system at the constant state and the energy method to the compressible MHD equations, then we get the optimal convergence rates of any order spatial derivatives (including the highest-order derivatives) of the solution. This result concern with the optimal time decay rates of the solutions, which extends the work obtained by Chen [5] for the compressible Navier-Stokes equations in R-3 to the 3D compressible MHD equations. Moreover, we have expanded the range of sfrom (0, 3/2] to [0, 5/2], compared with the previous results on optimal decay rates of global strong solutions for the 3D isentropic compressible MHD system. (C) 2021 Elsevier Inc. All rights reserved.
Keyword ：
Compressible MHD equations Compressible MHD equations Highest-order derivatives Highest-order derivatives Optimal time decay rates Optimal time decay rates Semigroup theory Semigroup theory
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| GB/T 7714 | Huang, Wenting , Lin, Xueyun , Wang, Weiwei . Decay-in-time of the highest-order derivatives of solutions for the compressible isentropic MHD equations [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2021 , 502 (2) . |
| MLA | Huang, Wenting et al. "Decay-in-time of the highest-order derivatives of solutions for the compressible isentropic MHD equations" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 502 . 2 (2021) . |
| APA | Huang, Wenting , Lin, Xueyun , Wang, Weiwei . Decay-in-time of the highest-order derivatives of solutions for the compressible isentropic MHD equations . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2021 , 502 (2) . |
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We investigate the effect of (interface) surface tensor on the linear Rayleigh-Taylor (RT) instability in stratified incompressible viscous fluids. The existence of linear RT instability solutions with largest growth rate Lambda is proved under the instability condition (i.e., the surface tension coefficient upsilon is less than a threshold upsilon(c)) by the modified variational method of PDEs. Moreover, we find a new upper bound for Lambda. In particular, we directly observe from the upper bound that Lambda decreasingly converges to zero as upsilon goes from zero to the threshold upsilon(c).
Keyword ：
Incompressible fluids Incompressible fluids Rayleigh-Taylor instability Rayleigh-Taylor instability Stratified viscous fluids Stratified viscous fluids Surface tension Surface tension
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| GB/T 7714 | Dou, Changsheng , Wang, Jialiang , Wang, Weiwei . A new upper bound for the largest growth rate of linear Rayleigh-Taylor instability [J]. | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2021 , 2021 (1) . |
| MLA | Dou, Changsheng et al. "A new upper bound for the largest growth rate of linear Rayleigh-Taylor instability" . | JOURNAL OF INEQUALITIES AND APPLICATIONS 2021 . 1 (2021) . |
| APA | Dou, Changsheng , Wang, Jialiang , Wang, Weiwei . A new upper bound for the largest growth rate of linear Rayleigh-Taylor instability . | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2021 , 2021 (1) . |
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